共查询到20条相似文献,搜索用时 31 毫秒
1.
Thomas Schick 《Mathematische Annalen》2000,317(4):727-750
The Atiyah conjecture predicts that the -Betti numbers of a finite CW-complex with torsion-free fundamental group are integers. We establish the Atiyah conjecture, under the condition that it
holds for G and that is a normal subgroup, for amalgamated free products . Here F is a free group and is an arbitrary semi-direct product. This includes free products G*F and semi-direct products . We also show that the Atiyah conjecture holds (with an additional technical condition) for direct and inverse limits of
groups for which it is true. As a corollary it holds for positive 1-relator groups with torsion free abelianization. Putting
everything together we establish a new (bigger) class of groups for which the Atiyah conjecture holds, which contains all
free groups and in particular is closed under taking subgroups, direct sums, free products, extensions with torsion-free elementary
amenable quotient or with free quotient, and under certain direct and inverse limits.
Received: 22 August 1998/ Revised: 10 Jannary 2000 / Published online: 28 June 2000 相似文献
2.
The algebra Bp(\Bbb R){\cal B}_p({\Bbb R}), p ? (1,¥)\{2}p\in (1,\infty )\setminus \{2\}, consisting of all measurable sets in \Bbb R{\Bbb R} whose characteristic function is a Fourier p-multiplier, forms an algebra of sets containing many interesting and non-trivial elements (e.g. all intervals and their finite unions, certain periodic sets, arbitrary countable unions of dyadic intervals, etc.). However, Bp(\Bbb R){\cal B}_p({\Bbb R}) fails to be a s\sigma -algebra. It has been shown by V. Lebedev and A. Olevskii [4] that if E ? Bp(\Bbb R)E\in {\cal B}_p({\Bbb R}), then E must coincide a.e. with an open set, a remarkable topological constraint on E. In this note we show if $2 < p < \infty $2 < p < \infty , then there exists E ? Bp(\Bbb R)E\in {\cal B}_p({\Bbb R}) which is not in Bq(\Bbb R){\cal B}_q({\Bbb R}) for any q > pq>p. 相似文献
3.
Let G be a group and $\pi$ be a set of primes. We consider the set ${\rm cd}^{\pi}(G)$ of
character degrees of G that are divisible only by primes in $\pi$. In particular, we define
$\Gamma^{\pi}(G)$ to be the graph whose vertex set is the set of primes dividing degrees in ${\rm cd}^{\pi}(G)$. There is an edge between
p and q if pq divides a degree
$a \in {\rm cd}^{\pi}(G)$. We show that if G is $\pi$-solvable, then
$\Gamma^{\pi}(G)$ has at most two connected components. 相似文献
4.
By a totally regular parallelism of the real projective 3-space
P3:=PG(3, \mathbb R){\Pi_3:={{\rm PG}}(3, \mathbb {R})} we mean a family T of regular spreads such that each line of Π
3 is contained in exactly one spread of T. For the investigation of totally regular parallelisms the authors mainly employ Klein’s correspondence λ of line geometry and the polarity π
5 associated with the Klein quadric H
5 (for details see Chaps. 1 and 3). The λ-image of a totally regular parallelism T is a hyperflock of H
5, i.e., a family H of elliptic subquadrics of H
5 such that each point of H
5 is on exactly one subquadric of H. Moreover, {p5(span l(X))|X ? T}=:HT{\{\pi_5({{\rm span}} \,\lambda(\mathcal {X}))\vert\mathcal {X}\in\bf{T}\}=:\mathcal {H}_{\bf{T}}} is a hyperflock determining line set, i.e., a set Z{\mathcal {Z}} of 0-secants of H
5 such that each tangential hyperplane of H
5 contains exactly one line of Z{\mathcal {Z}} . We say that dim(span HT)=:dT{{{\rm dim}}({{\rm span}}\,\mathcal {H}_{\bf{T}})=:d_{\bf{T}}} is the dimension of
T and that T is a d
T
- parallelism. Clifford parallelisms and 2-parallelisms coincide. The examples of non-Clifford parallelisms exhibited in Betten
and Riesinger [Result Math 47:226–241, 2004; Adv Geom 8:11–32, 2008; J Geom (to appear)] are totally regular and of dimension
3. If G{\mathcal{G}} is a hyperflock determining line set, then {l-1 (p5(X) ?H5) | X ? G}{\{\lambda^{-1}\,{\rm (}\pi_5(X){\,\cap H_5)\,|\, X\in\mathcal{G}\}}} is a totally regular parallelism. In the present paper the authors construct examples of topological (see Definition 1.1)
4- and 5-parallelisms via hyperflock determining line sets. 相似文献
5.
The notion of pseudo-randomness of subsets of
\mathbb Zn{\mathbb Z_n} is defined, and the measures of pseudo-randomness are introduced. Then a construction (based on the use of hybrid character
sums) will be presented for subsets of
\mathbb Zp{\mathbb Z_p} with strong pseudo-random properties. 相似文献
6.
Martin R. Bridson 《Mathematische Annalen》2000,317(4):629-633
Abstract. We construct finitely presented subgroups of GL that have infinitely many conjugacy classes of finite subgroups. This answers a question of Grunewald and Platonov. We suggest
a variation on their question.
Received: 26 August 1999 / Revised: 28 September 1999 / Published online: 8 May 2000 相似文献
7.
Masao Yamazaki 《Mathematische Annalen》2000,317(4):635-675
Abstract. We consider the Navier-Stokes equations with time-dependent external force, either in the whole time or in positive time
with initial data, with domain either the whole space, the half space or an exterior domain of dimension . We give conditions on the external force sufficient for the unique existence of small solutions in the weak- space bounded for all time. In particular, this result gives sufficient conditions for the unique existence and the stability
of small time-periodic solutions or almost periodic solutions. This result generalizes the previous result on the unique existence
and the stability of small stationary solutions in the weak- space with time-independent external force.
Received: 30 March 1999 / Accepted: 21 September 1999 / Published online: 28 June 2000 相似文献
8.
Let G be a finitely presented pro-
C{\cal C}
group with discrete relations. We prove that the kernel of an epimorphism of G to
[^(\Bbb Z)]C\hat{\Bbb Z}_{\cal C}
is topologically finitely generated if G does not contain a free pro-
C{\cal C}
group of rank 2. In the case of pro-p groups the result is due to J. Wilson and E. Zelmanov and does not require that the relations are discrete ([15], [17]).For a pro-p group G of type FPm we define a homological invariant C{\cal C}
groups, pro-p groups, homological type FPm, finite presentabilityBoth authors are partially supported by CNPq, Brazil. 相似文献
9.
B. C. Grecu G. A. Mu?oz-Fernández J. B. Seoane-Sepúlveda 《Mathematische Zeitschrift》2009,263(4):775-785
Let H be a two-dimensional complex Hilbert space and P(3H){{\mathcal P}(^3H)} the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, BP(3H){{\mathsf B}_{{\mathcal P}(^3H)}} , from which we deduce that the unit sphere of P(3H){{\mathcal P}(^3H)} is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of BP(3H){{\mathsf B}_{{\mathcal P}(^3H)}} remains extreme as considered as an element of BL(3H){{\mathsf B}_{{\mathcal L}(^3H)}} . Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H){{\mathcal P}(^3H)} and give a characterization of its smooth points. 相似文献
10.
Bernhard Burgstaller 《Monatshefte für Mathematik》2009,157(1):1-11
There exists a separable exact C*-algebra A which contains all separable exact C*-algebras as subalgebras, and for each norm-dense measure μ on A and independent μ-distributed random elements x
1, x
2, ... we have . Further, there exists a norm-dense non-atomic probability measure μ on the Cuntz algebra such that for an independent sequence x
1, x
2, ... of μ-distributed random elements x
i
we have . We introduce the notion of the stochastic rank for a unital C*-algebra and prove that the stochastic rank of C([0, 1]
d
) is d.
B. Burgstaller was supported by the Austrian Schr?dinger stipend J2471-N12. 相似文献
11.
Given a finite subset
A{\cal A}
of an additive group
\Bbb G{\Bbb G}
such as
\Bbb Zn{\Bbb Z}^n
or
\Bbb Rn{\Bbb R}^n
, we are interested in efficient covering of
\Bbb G{\Bbb G}
by translates of
A{\cal A}
, and efficient packing of translates of
A{\cal A}
in
\Bbb G{\Bbb G}
. A set
S ì \Bbb G{\cal S} \subset {\Bbb G}
provides a covering if the translates
A + s{\cal A} + s
with
s ? Ss \in {\cal S}
cover
\Bbb G{\Bbb G}
(i.e., their union is
\Bbb G{\Bbb G}
), and the covering will be efficient if
S{\cal S}
has small density in
\Bbb G{\Bbb G}
. On the other hand, a set
S ì \Bbb G{\cal S} \subset {\Bbb G}
will provide a packing if the translated sets
A + s{\cal A} + s
with
s ? Ss \in {\cal S}
are mutually disjoint, and the packing is efficient if
S{\cal S}
has large density.
In the present part (I) we will derive some facts on these concepts when
\Bbb G = \Bbb Zn{\Bbb G} = {\Bbb Z}^n
, and give estimates for the minimal covering densities and maximal packing densities of finite sets
A ì \Bbb Zn{\cal A} \subset {\Bbb Z}^n
. In part (II) we will again deal with
\Bbb G = \Bbb Zn{\Bbb G} = {\Bbb Z}^n
, and study the behaviour of such densities under linear transformations. In part (III) we will turn to
\Bbb G = \Bbb Rn{\Bbb G} = {\Bbb R}^n
. 相似文献
12.
Jiabao Su 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,21(2):51-62
We study the existence and multiplicity of nontrivial radial solutions of the quasilinear equation
{ll-div(|?u|p-2?u)+V(|x|)|u|p-2u=Q(|x|)f(u), x ? \mathbbRN,u(x) ? 0, |x|? ¥\left\{\begin{array}{ll}-{div}(|\nabla u|^{p-2}\nabla u)+V(|x|)|u|^{p-2}u=Q(|x|)f(u),\quad x\in \mathbb{R}^N,\\u(x) \rightarrow 0, \quad |x|\rightarrow \infty \end{array}\right. 相似文献
13.
Bernhard Burgstaller 《Monatshefte für Mathematik》2009,265(4):1-11
There exists a separable exact C*-algebra A which contains all separable exact C*-algebras as subalgebras, and for each norm-dense measure μ on A and independent μ-distributed random elements x
1, x
2, ... we have
limn ? ¥\mathbb P(C*(x1,?,xn) is nuclear)=0{\rm {lim}}_{n \rightarrow \infty}\mathbb {P}(C^*(x_1,\ldots,x_n) \mbox{ is nuclear})=0. Further, there exists a norm-dense non-atomic probability measure μ on the Cuntz algebra O2{\mathcal {O}_2} such that for an independent sequence x
1, x
2, ... of μ-distributed random elements x
i
we have
lim infn ? ¥\mathbb P(C*(x1,?,xn) is nuclear)=0{\rm {lim\, inf}}_{n \rightarrow \infty}\mathbb {P}(C^*(x_1,\ldots,x_n) \mbox{ is nuclear})=0. We introduce the notion of the stochastic rank for a unital C*-algebra and prove that the stochastic rank of C([0, 1]
d
) is d. 相似文献
14.
In this paper, we establish several decidability results for pseudovariety joins of the form
\sf Vú\sf W{\sf V}\vee{\sf W}
, where
\sf V{\sf V}
is a subpseudovariety of
\sf J{\sf J}
or the pseudovariety
\sf R{\sf R}
. Here,
\sf J{\sf J}
(resp.
\sf R{\sf R}
) denotes the pseudovariety of all
J{\cal J}
-trivial (resp.
?{\cal R}
-trivial) semigroups. In particular, we show that the pseudovariety
\sf Vú\sf W{\sf V}\vee{\sf W}
is (completely) κ-tame when
\sf V{\sf V}
is a subpseudovariety of
\sf J{\sf J}
with decidable κ-word problem and
\sf W{\sf W}
is (completely) κ-tame. Moreover, if
\sf W{\sf W}
is a κ-tame pseudovariety which satisfies the pseudoidentity x1 ⋯ xryω+1ztω = x1 ⋯ xryztω, then we prove that
\sf Rú\sf W{\sf R}\vee{\sf W}
is also κ-tame. In particular the joins
\sf Rú\sf Ab{\sf R}\vee{\sf Ab}
,
\sf Rú\sf G{\sf R}\vee{\sf G}
,
\sf Rú\sf OCR{\sf R}\vee{\sf OCR}
, and
\sf Rú\sf CR{\sf R}\vee{\sf CR}
are decidable. 相似文献
15.
Hongsen Chen Zhangxin Chen Baoyan Li 《Numerical Methods for Partial Differential Equations》2003,19(4):525-553
This article studies the stability and convergence of the hp version of the three families of mixed discontinuous finite element (MDFE) methods for the numerical solution of reaction‐diffusion problems. The focus of this article is on these problems for one space dimension. Error estimates are obtained explicitly in the grid size h, the polynomial degree p, and the solution regularity; arbitrary space grids and polynomial degree are allowed. These estimates are asymptotically optimal in both h and p for some of these methods. Extensive numerical results to show convergence rates in h and p of the MDFE methods are presented. Theoretical and numerical comparisons between the three families of MDFE methods are described. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 525–553, 2003 相似文献
16.
Dan Yasaki 《Selecta Mathematica, New Series》2006,12(3-4):541-564
Let X = Γ \G/ K be an arithmetic quotient of a symmetric space of non-compact type. In the case that G has
-rank 1, we construct Γ-equivariant deformation retractions of D = G/K onto a set D0. We prove that D0 is a spine, having dimension equal to the virtual cohomological dimension of Γ. In fact, there is a (k − 1)-parameter family of such deformation retractions, where k is the number of Γ -conjugacy classes of rational parabolic subgroups of G. The construction of the spine also gives a way to construct an exact fundamental domain for Γ. 相似文献
17.
18.
The main purpose of this paper is to prove the following result. Let R be a 2-torsion free semiprime ring with symmetric Martindale ring of quotients Q
s
and let q{\theta} and f{\phi} be automorphisms of R. Suppose T:R? R{T:R\rightarrow R} is an additive mapping satisfying the relation T(xyx)=T(x)q(y)q(x)-f(x)T(y)q(x)+f(x)f(y)T(x){T(xyx)=T(x)\theta (y)\theta (x)-\phi (x)T(y)\theta (x)+\phi (x)\phi (y)T(x)}, for all pairs x,y ? R{x,y\in R}. In this case T is of the form 2T(x)=qq(x)+f(x)q{2T(x)=q\theta (x)+\phi (x)q}, for all x ? R{x\in R} and some fixed element q ? Qs{q\in Q_{s}}. 相似文献
19.
We study Stickelberger elements associated to -extensions over global function fields of characteristic p>0 and show that they are in some sense generically irreducible in the Iwasawa algebras. 相似文献
20.
Emmanuel Giner 《Set-Valued Analysis》2007,15(2):125-138
We give complete characterizations of integral functionals which are Lipschitzian on a Lebesgue space L
p
with p ≠ ∞. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue
spaces. In every cases, the Lipchitzian properties of the integral functional can be described by growth conditions on the
subdifferentials of the integrand which are equivalent to Lipschitzian properties of the integrand.
相似文献
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